Prime factorization of $$$3196$$$
Your Input
Find the prime factorization of $$$3196$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$3196$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$3196$$$ by $$${\color{green}2}$$$: $$$\frac{3196}{2} = {\color{red}1598}$$$.
Determine whether $$$1598$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$1598$$$ by $$${\color{green}2}$$$: $$$\frac{1598}{2} = {\color{red}799}$$$.
Determine whether $$$799$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$799$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$799$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$799$$$ is divisible by $$$7$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$11$$$.
Determine whether $$$799$$$ is divisible by $$$11$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$13$$$.
Determine whether $$$799$$$ is divisible by $$$13$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$17$$$.
Determine whether $$$799$$$ is divisible by $$$17$$$.
It is divisible, thus, divide $$$799$$$ by $$${\color{green}17}$$$: $$$\frac{799}{17} = {\color{red}47}$$$.
The prime number $$${\color{green}47}$$$ has no other factors then $$$1$$$ and $$${\color{green}47}$$$: $$$\frac{47}{47} = {\color{red}1}$$$.
Since we have obtained $$$1$$$, we are done.
Now, just count the number of occurences of the divisors (green numbers), and write down the prime factorization: $$$3196 = 2^{2} \cdot 17 \cdot 47$$$.
Answer
The prime factorization is $$$3196 = 2^{2} \cdot 17 \cdot 47$$$A.